To determine the linear equation that represents Esther's monthly pay rate, we need to account for two components of her earnings: her hourly wage and the fixed monthly travel allowance.
Let's define the variables:
- [tex]\( x \)[/tex] represents the number of hours Esther works in a month.
- [tex]\( y \)[/tex] represents Esther's total monthly pay.
### Step-by-Step Solution:
1. Hourly Wage:
- Esther earns \[tex]$12 per hour.
- Therefore, for \( x \) hours worked in a month, her earnings from hours worked would be \( 12x \).
2. Fixed Monthly Travel Allowance:
- Esther receives a fixed travel allowance of \$[/tex]50 every month.
- This amount is not dependent on the number of hours worked and is a constant.
3. Total Monthly Pay:
- Her total monthly pay [tex]\( y \)[/tex] is the sum of her earnings from hours worked and the travel allowance.
- Thus, the equation for her total monthly earnings is:
[tex]\[
y = 12x + 50
\][/tex]
### Choosing the Correct Answer:
Given the options:
A. [tex]\( y = 50x + 12 \)[/tex]
B. [tex]\( y = 12x + 50 \)[/tex]
C. [tex]\( y = 12x \)[/tex]
D. [tex]\( y = 50x \)[/tex]
The correct linear equation that represents Esther's monthly pay rate is:
B. [tex]\( y = 12x + 50 \)[/tex]
